In this thesis, we shall reexamine and provide as clear an exposition as possible of a method presented by P. R. Garabedian which results in an integral formula representation of a solution to the wave equation. The method involves analytically extending a harmonic function of real arguments along a purely imaginary axis in complex space and establishing the validity of the standard integral formula for harmonic functions as a representation of a solution to the Wave equation when one of the arguments is purely imaginary. This is done in the odd dimensional case by integration by parts and an application of the residue theorem, and in the even dimensional case by computing bounds on the integrals.